Collaborative Research: Multiscale Aspects for Wave Propagation Inverse Problems

许多天然材料在广泛的尺度上表现出结构的非均质性。这种具有微观结构的介质的例子几乎包括地壳的每一部分，以及制造的复合材料，如混凝土。这些材料也支持波动运动，并且各种技术已经发展到使用传播波进行材料结构的无损整合。在目前的状态下，这些技术（反射地震学、超声波无损评估等）在很大程度上是基于对均匀（或近均匀）材料中的波的理论认识和计算方法。有效介质理论试图在宏观尺度上表达微观异质性的影响，在一定程度上弥补了理论基础和应用背景之间的鸿沟。然而，有效介质方法的严格证明在很大程度上仅限于周期性材料模型，这种模型不像沉积岩这样的无序材料。本研究将尝试利用具有微观结构的介质中声学和弹性波模拟的最新进展，以评估通过无微观结构的更简单模型来解释模拟实验数据的可行性。这些模型可能表现出微观尺度上不存在的物理特征，例如粘性损失或各向异性响应。我们的方法结合了各种数值模拟方法，包括数值升级，用于计算高度非均质模型中的波，并通过反演或参数估计来确定宏观模型。提出的工作将依赖于以前开发的反演计算框架。对于科学家来说，要想开采石油和天然气，预测地震和海啸等其他构造事件，安全地修复污染物，并将多余的温室气体埋在地下，他们首先必须能够对地球的地下进行成像。岩层、流体和断层需要绘制地图，了解它们的深度和横向范围。为了获得地下的图像，能量被传送到地下，从而产生波。由于地下的非均匀性，部分地震波被送回地表，地震仪（麦克风）在地震波经过时将其记录下来。科学家们试图从这些信号推断地下的结构。由于岩石是由多孔晶格中的微观颗粒组成的，其非常复杂的力学性质使这一推论变得极其复杂。这些微小成分的物理特性和孔隙内的流体以一种复杂而鲜为人知的方式结合在一起，产生了地球的可观测响应。在我们之前的工作中，我们设计了模拟波在复杂微观结构材料中的传播的方法，以及从可观测数据中确定宏观材料描述的程序。该提案设想了这两种工作的融合，并可以阐明从地震记录中可以或不能推断出地下结构的哪些方面。

Many natural materials exhibit structural heterogeneity across a wide range of scales. Examples of such media with microstructure include virtually every part of the Earth's crust, and manufactured composite materials such as concrete. These materials also support wave motion, and various technologies have evolved which use propagating waves for nondestructive interogation of material structure. In their present state, these technologies (reflection seismology, ultrasonic nondestructive evaluation, etc) are for the most part based on theoretical understanding and computational methods developed for waves in homogeneous (or near-homogeneous) materials. This divide between theoretical basis and application context is bridged to some extent by effective medium theories which attempt to express at macroscopic scales the effect of microscopic heterogeneities. However rigorous justification of the effective medium approach is largely limited to periodic material models, which do not resemble disordered materials such as sedimentary rock. This study will attempt to leverage recent advances in the simulation of acoustic and elastic waves in media with microstructure to assess the feasibility of explaining simulated experimental data by means of simpler models without microstructure. These models may exhibit physical characteristics not present on the microscopic scale, for instance viscous loss or anisotropic response. Our approach combines various numerial simulation methods, including numerical upscaling, for computing waves in highly heterogeneous models, with inversion or parameter estimation to determine macroscopic models. The proposed work will rely upon a previously developed computational framework for inversion. For scientists to be able to produce oil and gas, to predict earthquakes and other tectonic events such as tsunamis, to safely remediate contaminants, and to bury excess greenhouse gases underground, they must first be able to image the earth's subsurface. Rock layers, fluids, and faults need to be mapped and their depths and lateral extent understood. To create an image of the subsurface, energy is sent into the ground which generates a wave. The heterogeneous nature of the subsurface causes a portion of these waves to be sent back to the surface where seismometers (microphones) record the waves as they pass. From these signals scientists try to infer the structure of the subsurface. This inference is enormously complicated by the very complex mechanical nature of rock, which is composed of microscopic grain particles in a porous lattice. The physical characteristics of these tiny constituents and the fluids within the pores combine in a complex and poorly understood way to yield the observable response of the Earth. In our previous work, we have devised methods to simulate propagation of waves through complex microscopically structured material, and also procedures to determine the macroscopic material descriptions from observable data. This proposal envisions the fusion of these two lines of work and could shed light on which aspects of subsurface structure can, or can't, be inferred from seismic recordings.